Mathematics at the Frontiers of Science

Liquid crystal displays, nanoscale drug delivery devices, immunology and even rocket science. What do they have in common? Mathematics.

The Center for Nonlinear Analysis (CNA), Carnegie Mellon’s flagship applied math center, is celebrating its 15th anniversary September 8–10, with the conference “Frontiers in Applied Analysis,” which is bringing together an impressive group of preeminent mathematicians whose innovative work places them at the leading edge of the field of applied analysis. Conference speakers include Louis Nirenberg, winner of the Crafoord Prize and the National Medal of Science, and Pierre-Louis Lions, who was awarded the Fields Medal in 1994.

“These speakers are using highly original mathematics to solve a host of problems,” said David Kinderlehrer, a professor of mathematics at Carnegie Mellon and a conference organizer. “The fact that they will all be gathered under one roof speaks to the importance of applied analysis and to the eminence of the CNA.”

The goal of the CNA, which is supported by the National Science Foundation, is to identify and develop new applications of mathematics, promoting collaboration between applied mathematicians and allied scientists. The long-standing emphasis of the CNA research program has been on the study of mathematical models issuing from materials science. In recent years, the CNA has begun to respond to challenges in finance and biological sciences.

“With few resources, the CNA has become extremely prominent, building an international reputation in training and research, especially in the exploration of research at the frontiers of science,” said Irene Fonseca, Mellon College of Science Professor of Mathematics and Director of the CNA.

The organizers of the Frontiers in Applied Analysis conference hope that it will allow members of the CNA to examine what directions the field of mathematics is taking and to provide perspective for the center as it sets directions for its own initiatives. The conference also should allow presenters and attendees, including senior faculty, post-docs, and graduate and undergraduate students, to share ideas and possibly form new collaborations, according to Kinderlehrer.

In his talk, Louis Nirenberg, a professor at New York University’s Courant Institute of Mathematical Sciences, will discuss symmetries of convex bodies. Pierre-Louis Lions, a professor at the Collège de France, will review during his talk mathematical results on the chain of models for atoms and molecules, crystals and solids and continuum mechanics. Emmanuele DiBenedetto, another speaker at the conference and a professor at Vanderbilt University, will discuss mathematical simulations of the visual transduction pathway, the complex cascade of events by which cells in the eye convert light signals into nerve impulses. His work, like the work of many of the other conference speakers, lies at the interface of mathematics and biology.

For a complete list of conference speakers, a lecture schedule and registration information, go to the conference web site.